Multi-Matrix Models: Integrability Properties and Topological Content

We analyze multi--matrix chain models. They can be considered as multi--component Toda lattice hierarchies subject to suitable coupling conditions. The extension of such models to include extra discrete states requires a weak form of integrability. The discrete states of the $q$--matrix model are organized in representations of $sl_q$. We solve exactly the Gaussian--type models, of which we compute several all-genus correlators. Among the latter models one can classify also the discretized $c=1$ string theory, which we revisit using Toda lattice hierarchy methods. Finally we analyze the topological field theory content of the $2q$--matrix models: we define primary fields (which are $\infty^q$), metrics and structure constants and prove that they satisfy the axioms of topological field theories. We outline a possible method to extract interesting topological field theories with a finite number of primaries.Comment: 31 pages, Late

Toda lattice realization of integrable hierarchies

We present a new realization of scalar integrable hierarchies in terms of the Toda lattice hierarchy. In other words, we show on a large number of examples that an integrable hierarchy, defined by a pseudodifferential Lax operator, can be embedded in the Toda lattice hierarchy. Such a realization in terms the Toda lattice hierarchy seems to be as general as the Drinfeld--Sokolov realization.Comment: 11 pages, Latex (minor changes, to appear in Lett.Math.Phys.

Hamiltonian Structures of the Multi-Boson KP Hierarchies, Abelianization and Lattice Formulation

We present a new form of the multi-boson reduction of KP hierarchy with Lax operator written in terms of boson fields abelianizing the second Hamiltonian structure. This extends the classical Miura transformation and the Kupershmidt-Wilson theorem from the (m)KdV to the KP case. A remarkable relationship is uncovered between the higher Hamiltonian structures and the corresponding Miura transformations of KP hierarchy, on one hand, and the discrete integrable models living on {\em refinements} of the original lattice connected with the underlying multi-matrix models, on the other hand. For the second KP Hamiltonian structure, worked out in details, this amounts to finding a series of representations of the nonlinear \hWinf algebra in terms of arbitrary finite number of canonical pairs of free fields.Comment: 12 pgs, (changes in abstract, intro and outlook+1 ref added). LaTeX, BGU-94 / 1 / January- PH, UICHEP-TH/94-

Free field representation of Toda field theories

We study the following problem: can a classical $sl_n$ Toda field theory be represented by means of free bosonic oscillators through a Drinfeld--Sokolov construction? We answer affirmatively in the case of a cylindrical space--time and for real hyperbolic solutions of the Toda field equations. We establish in fact a one--to--one correspondence between such solutions and the space of free left and right bosonic oscillators with coincident zero modes. We discuss the same problem for real singular solutions with non hyperbolic monodromy.Comment: 29 pages, Latex, SISSA-ISAS 210/92/E

Generalized q-deformed Correlation Functions as Spectral Functions of Hyperbolic Geometry

We analyse the role of vertex operator algebra and 2d amplitudes from the point of view of the representation theory of infinite dimensional Lie algebras, MacMahon and Ruelle functions. A p-dimensional MacMahon function is the generating function of p-dimensional partitions of integers. These functions can be represented as amplitudes of a two-dimensional c=1 CFT. In this paper we show that p-dimensional MacMahon functions can be rewritten in terms of Ruelle spectral functions, whose spectrum is encoded in the Patterson-Selberg function of three dimensional hyperbolic geometry.Comment: 12 pages, no figure

Liouville and Toda field theories on Riemann surfaces

We study the Liouville theory on a Riemann surface of genus g by means of their associated Drinfeld--Sokolov linear systems. We discuss the cohomological properties of the monodromies of these systems. We identify the space of solutions of the equations of motion which are single--valued and local and explicitly represent them in terms of Krichever--Novikov oscillators. Then we discuss the operator structure of the quantum theory, in particular we determine the quantum exchange algebras and find the quantum conditions for univalence and locality. We show that we can extend the above discussion to $sl_n$ Toda theories.Comment: 41 pages, LaTeX, SISSA-ISAS 27/93/E

Genetics of familial non-medullary thyroid carcinoma (FNMTC)

Non-medullary thyroid carcinoma (NMTC) is the most frequent endocrine tumor and originates from the follicular epithelial cells of the thyroid. Familial NMTC (FNMTC) has been defined in pedigrees where two or more first-degree relatives of the patient present the disease in absence of other predisposing environmental factors. Compared to sporadic cases, FNMTCs are often multifocal, recurring more frequently and showing an early age at onset with a worse out-come. FNMTC cases show a high degree of genetic heterogeneity, thus impairing the identification of the underlying molecular causes. Over the last two decades, many efforts in identifying the susceptibility genes in large pedigrees were carried out using linkage-based approaches and genome-wide association studies, leading to the identification of susceptibility loci and variants associated with NMTC risk. The introduction of next-generation sequencing technologies has greatly contrib-uted to the elucidation of FNMTC predisposition, leading to the identification of novel candidate variants, shortening the time and cost of gene tests. In this review we report the most significant genes identified for the FNMTC predisposition. Integrating these new molecular findings in the clinical data of patients is fundamental for an early detection and the development of tailored ther-apies, in order to optimize patient management

BRST analysis of topologically massive gauge theory: novel observations

A dynamical non-Abelian 2-form gauge theory (with B \wedge F term) is endowed with the "scalar" and "vector" gauge symmetry transformations. In our present endeavor, we exploit the latter gauge symmetry transformations and perform the Becchi-Rouet-Stora-Tyutin (BRST) analysis of the four (3 + 1)-dimensional (4D) topologically massive non-Abelian 2-form gauge theory. We demonstrate the existence of some novel features that have, hitherto, not been observed in the context of BRST approach to 4D (non-)Abelian 1-form as well as Abelian 2-form and 3-form gauge theories. We comment on the differences between the novel features that emerge in the BRST analysis of the "scalar" and "vector" gauge symmetries of the theory.Comment: LaTeX file, 14 pages, an appendix added, references expanded, version to appear in EPJ

Hawking Radiation for Scalar and Dirac Fields in Five Dimensional Dilatonic Black Hole via Anomalies

We study massive scalar fields and Dirac fields propagating in a five dimensional dilatonic black hole background. We expose that for both fields the physics can be describe by a two dimensional theory, near the horizon. Then, in this limit, by applying the covariant anomalies method we find the Hawking flux by restoring the gauge invariance and the general coordinate covariance, which coincides with the flux obtained from integrating the Planck distribution for fermions.Comment: 10 page

Aberration cancellation in quantum interferometry

We report the first experimental demonstration of even-order aberration cancellation in quantum interferometry. The effect is a spatial counterpart of the spectral group velocity dispersion cancellation, which is associated with spectral entanglement. It is manifested in temporal interferometry by virtue of the multi-parameter spatial-spectral entanglement. Spatially-entangled photons, generated by spontaneous parametric down conversion, were subjected to spatial aberrations introduced by a deformable mirror that modulates the wavefront. We show that only odd-order spatial aberrations affect the quality of quantum interference